Universal diffusive decay of correlations in gapped one-dimensional systems

We apply a semiclassical approach to express finite temperature dynamical correlation functions of gapped spin models analytically. We show that the approach of [Á. Rapp, G. Zaránd, Phys. Rev. B 74, 014433 (2006)] can also be used for the S = 1 antiferromagnetic Heisenberg chain, whose lineshape can be measured experimentally. We generalize our calculations to O(N) quantum spin models and the sineGordon model in one dimension, and show that in all these models, the finite temperature decay of certain correlation functions is characterized by the same universal semiclassical relaxation function. PACS. 75.10.Pq Spin chain models – 05.30.-d Quantum statistical mechanics – 05.50.+q Lattice theory and statistics